name,objects_hr,arrows_hr
1,(is) the point,(is) the identity arrow
nCob,(n-1)-dimensional compact oriented manifolds,n-dimensional cobordisms
2Cat,2-categories,2-functors
AbCat,Abelian categories,right exact functors
Ab,Abelian groups,group maps
AbTor,Abelian torsion groups,group maps
BanAlg,Banach algebras,short linear maps
BanRing,Banach rings,short group maps
Ban_k,Banach spaces over fields k,short linear maps
BoolAlg,Boolean algebras,lattice maps
CW,CW complexes,cellular maps
CartSp,Cartesian spaces,smooth maps
Feyn,Feynman diagrams,symmetries of Feynman diagrams
Haus,Hausdorff (T₂) spaces,continuous maps
HeytAlg,Heyting algebras,lattice maps
Hilb,Hilbert spaces,short linear maps
Hilb₀,Hilbert spaces,unitary operators
LMet,Lawvere metric spaces,short maps
SupLieAlg_k,Lie algebras over super vector spaces over fields k,super linear maps
LieAlg_k,Lie algebras over vector spaces over fields k,linear maps
LieGrp,Lie groups,smooth group maps
LieRing,Lie rings,group maps
Stone,Stone spaces,continuous maps
Tor,Torsion groups,group maps
Tych,Tychonoff spaces,continuous maps
AdicRing,adic rings,continuous ring maps
AdmRep,admissible domain representations,representable continuous maps
Alg(Ab),algebras of monoids in Ab (rings),algebra maps
Ass,assemblies,computable maps
BiCat,bicategories,pseudofunctors
BrMonCat,braided monoidal categories,lax monoidal functors
Cat,categories,functors
Ho(Cat),categories,natural isomorphism classes of functors
Prof,categories,profunctors
Ch.(Vect_k),chain complices of vector spaces,linear maps
CPROP,colored monoidal product & permutation categories,eso strict monoidal functors
AdicCRing,commutative adic rings,continuous ring maps
CommAlg(Ab),commutative algebras of monoids in Ab (rings),algebra maps
CMon,commutative monoids,monoid maps
CRing,commutative rings,ring maps
CompCat,compact closed categories,lax monoidal functors
DagCompCat,compact closed †-categories,lax monoidal †-functors
Comp,compacta (compact Hausdorff spaces),continuous maps
CompBoolAlg,complete Boolean algebras (CABAs),lattice maps
CompLat,complete lattices,lattice maps
CompMet,complete metric spaces,short maps
CompNormGrp,complete normed groups,short group maps
CPO,complete partial orders,Scott-continuous maps
KV,computable real numbers,computable maps
DSet,dendroidal sets,dendroidal maps
Diff,differentiable manifolds,continuous maps
DGCAlg,differential-graded commutative algebras of vector spaces,differential-graded algebra maps
DGph,digraphs,digraph maps
DirGph,directed graphs,graph maps
DCPO,directed-complete partial orders,Scott-continuous maps
DistLat,distributive lattices,lattice maps
DblCat,double categories,double functors
EffAdmRep,effective admissible domain representations,computable continuous maps
Field,fields,field maps
Hyp,finite directed hypergraphs,hypergraph maps
FinGrp,finite groups,group maps
FinMet,finite metric spaces,short maps
FinSet,finite sets,finite maps
FinVect_k,finite vector spaces over fields k,linear maps
FinVect_q,finite vector spaces over finite fields of order q,linear maps
FinHilb,finite-dimensional Hilbert spaces,short linear maps
Rex,finitely cocomplete categories,right exact functors
Lex,finitely complete categories,left exact functors
Frm,frames,frame maps
Grpd,groupoids,functors
Ho(Grpd),groupoids,natural isomorphism classes of functors
Span(Grpd),groupoids,spans of tame functors
Grp,groups,group maps
1Type,homotopy 1-types,continuous maps
Idem,idempotent endofunctions,idempotency-respecting maps
Mono,injections,commuting squares
Lat,lattices,lattice maps
Loc,locales,continuous maps
PrCat,locally presentable categories,left adjoint functors
Sierp,maps,commuting squares
Meas,measurable spaces,measurable maps
Met,metric spaces,short maps
Mod(Ab),modules of monoids in Ab (rings),module maps
MonCat,monoidal categories,lax monoidal functors
PROP,monoidal product & permutation categories,eso strict monoidal functors
Mon,monoids,monoid maps
Bimod(Ab),monoids in Ab (rings),bimodules of monoids in Ab (rings)
MultiSet,multisets,multimaps
R+,non-negative real numbers,addition
Rng,nonunital rings,nonunital ring maps
NormRing,normed (commutative) rings,short group maps
NormAb,normed Abelian groups,group maps
NormGrp,normed groups,short group maps
Ho(Eff),numbered sets,homotopy classes of computable maps
Op(FinCartSp),open sets of finite-dimensional Cartesian spaces,inclusions
Pos,partial orders,monotone maps
Cluster,partitioned sets,non-refinement-increasing maps
PermCat,permutative (symmetric strict monoidal) categories,multilinear functors
PDiff,piecewise-differentiable manifolds,piecewise-continuous maps
PL,piecewise-linear manifolds,piecewise-continuous maps
Set*,pointed sets,based maps